Finite Group DatabasebetaFinite Group Databasebeta| order | 8380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C419⋊AGL(1,𝔽5) |
| Fitting, socle, derived, Hall | C5×C419 ⋊ C4 |
| Sylow | C419 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ Dic419 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C419 | C4 |
| LCS | G ▷ C5×C419 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,419|a^2=b,c^a=c^2,d^a=d^418,c^b=c^4841 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C419⋊AGL(1,𝔽5), C3⋊(C419⋊AGL(1,𝔽5)) |
| maximal normal subgroup of | C3×C419⋊AGL(1,𝔽5) |
| maximal quotient of | C3×C419⋊AGL(1,𝔽5), C3⋊(C419⋊AGL(1,𝔽5)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8380, 7);